Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. What was Riya's score on the fourth physics test she took? (1) Her score on the fourth test was 12 points higher than her average (arithmetic mean) score on the first three tests she took. (2) Her score on the fourth test raised her average (arithmetic mean) test score from 87 to 90.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but none of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement (1) only gives a relationship between the fourth test score and the average of the first three tests, which is insufficient to find the exact score. Statement (2) provides the average of the first three tests (87) and the average of all four tests (90), allowing us to calculate the total score of the first three tests (261) and the total score of all four tests (360). The difference, 360 - 261 = 99, is the score of the fourth test, making Statement (2) alone sufficient.

AI explanation

Statement 2 alone provides the overall average before and after the fourth test, meaning the new average of 90 multiplied by 4 tests yields a total of 360 points. The old average of 87 multiplied by 3 tests yields a total of 261 points. The fourth test score is the difference between these totals, so 360 minus 261 equals 99. Because statement 1 lacks the actual numerical value of the first three test average, it cannot produce a specific score; therefore, statement 2 alone is sufficient.

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